Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes system in a half-space

TL;DR

This paper develops new estimates for solutions of the non-stationary Stokes system in a half-space using anisotropic Sobolev spaces with mixed norms, with applications to Navier-Stokes equations in three dimensions.

Contribution

It introduces novel anisotropic Sobolev space estimates for the Stokes system, including pressure, in a half-space setting, extending previous regularity results.

Findings

Derived new estimates for Stokes solutions with pressure.

Applied estimates to weak solutions of Navier-Stokes equations.

Extended Sobolev space regularity results in half-space domains.

Abstract

We are concerned with the non-stationary Stokes system with non-homogeneous external force and non-zero initial data in ${\mathbb R}^n_+ \times (0,T)$. We obtain new estimates of solutions including pressure in terms of mixed anisotropic Sobolev spaces. As an application, some anisotropic Sobolev estimates are presented for weak solutions of the Navier-Stokes equations in a half-space in dimension three.